Question

find the reference angle for - 105°.

Explanation:

Step1: Determine the positive - equivalent angle

Since the given angle is \(-105^{\circ}\), add \(360^{\circ}\) to get a positive - equivalent angle. \(-105^{\circ}+360^{\circ}=255^{\circ}\).

Step2: Identify the quadrant

The angle \(255^{\circ}\) lies in the third quadrant (\(180^{\circ}<255^{\circ}<270^{\circ}\)).

Step3: Calculate the reference angle

For an angle \(\theta\) in the third quadrant, the reference angle \(\theta_{r}=\theta - 180^{\circ}\). So, \(\theta_{r}=255^{\circ}-180^{\circ}=75^{\circ}\).

Answer:

\(75\)